Ideally, we could train SISVAE with a whole time series as input, and the model outputs the whole reconstruction. However, in many real applications, the time series is typically very long. The objective function Eq. REF  of our model is summed sequentially over time, such that computing the gradient of it requires back propagation over time [1]}. Researches [2]} observe that RNNs are hard to train when sequence length is over 200, the model may face the problem of vanishing gradients and exploding gradients, which is also undesirable for anomaly detection tasks.
